Sylvia has been saving for a down payment for the purchase of a condominium for 10 years. Monthly deposits of \$375 are made into an annuity that earns 4.25% annual interest, compounded monthly. According to account, documents, after these 10 years, there is a balance of \$55,952.72 in the account. How much interest has the account earned. Round the answer to the nearest cent.

الحلّ

S y l v ia ha s b ee n s a v in g f or a d o w n p a y m e n t f or t h e p u rc ha se o f a co n d o mini u m f or 10 ye a rs . M o n t h l y d e p os i t s o f $375 a re ma d e in t o an ann u i t y t ha t e a r n s 4.25% ann u a l in t eres t, co m p o u n d e d m o n t h l y . A ccor d in g t o a cco u n t, d oc u m e n t s, a f t er t h ese 10 ye a rs, t h ere i s a ba l an ce o f $55, 952.72 in t h e a cco u n t . Ho w m u c h in t eres t ha s t h e a cco u n t e a r n e d . R o u n d t h e an s w er t o t h e n e a res t ce n t .

Amount : 573.17

خطوات الحلّ

Translate the problem into an equation:

A = 375 (1 + \frac{0.0425}{12})^{12 \cdot 10}

375 (1 + \frac{0.0425}{12})^{12 \cdot 10} = 573.16589 \dots

Round to the nearest hundredth:

573.17

Amount : 573.17